The Bohnenblust-Hille inequality says that the 2m m+1 -norm of the coefficients of an m-homogeneous polynomial P on C n is bounded by P times a constant independent of n, where denotes the supremum norm on the polydisc D n . The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be C m for some C > 1.
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Defant et al. (2011) studied this question.